I am not sure chasing prestige is the least bit worthwhile. I’m pretty convinced it isn’t. But wanting to be surrounded by students excited by whatever they are studying is worthwhile. While there is obviously overlap in the types of students attending various schools there also tends to be a prevailing climate or personality, and frankly I’m too far removed from Geneseo these days to evaluate that school specifically, but you’d be hard put to find an critical mass of students at SUNY on fire about their academic pursuits. I can see craving that even if you encountered some problems in high school. You are most likely to get that at some of the schools some people think are prestigious-but not all. At some you will find the same grade grubbers you’ll find at a SUNY. The OP may not be the least interested in being in a place where students are excited about scholarly activity but I’m writing this for anyone in the future who might find them self in OP’s position and wants an intellectually energized campus.
So how can you transfer to one? Well the posters so far are making it all about GPA. Fair enough. That can work. You can follow suit, stay in that box, pray that a strong GPA with your scores will get you in and send out a slew of applications. Ho Hum squeeze a few more points out of your test score and go for extra credit…yawn…
Or you can start constructing a new academic trajectory that is likely to be attractive to colleges.